Structural stability of singular holomorphic foliations having a meromorphic first integral.(English)Zbl 0735.57014

From the introduction: “We give extensions of Reeb’s Stability Theorem to singular holomorphic foliations of codimension 1 having a meromorphic first integral and defined on projective manifolds $$\mathcal M$$ with $$H^ 1({\mathcal M},{\mathbb{C}})=0$$. (…) If the leaves form a Lefschetz pencil, then the foliation is $$C^ 0$$-structurally stable.”.

MSC:

 57R30 Foliations in differential topology; geometric theory 32S65 Singularities of holomorphic vector fields and foliations
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